$1\mathrm{.}5$ pts$.$ The circuit below does the error correction for one error. Explain the logic with the last gate. Also. Clearly and fully describe the purpose of the last three right$-$most gates.

Correcting Bit Flips

No errors, $|q_0{q}_1{q}_2$:$||000>|000>|000>|000>$

One Error

$|000|>|001|>|001|>|001|>|001|>$

$|000|>|010|>|010|>|010|>|010|>$

$|000|>|100|>|110|>|111|>|011|>$

Two errors $|000>|011>|011>|011>|111>$